Maximal δ-separated sets in separable metric spaces and weak forms of choice
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918286805958656 |
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| author | Dybowski, Michał Górka, Przemyslaw Howard, Paul |
| author_facet | Dybowski, Michał Górka, Przemyslaw Howard, Paul |
| contents | We show that the statement ``In every separable pseudometric space there is a maximal non-strictly δ-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and Górka in [M. Dybowski and P. Górka, The axiom of choice in metric measure spaces and maximal δ-separated sets, Archive for Mathematical Logic 62, 735-749, 2023.]. We also prove several related results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal δ-separated sets in separable metric spaces and weak forms of choice Dybowski, Michał Górka, Przemyslaw Howard, Paul Logic 03E25 (Primary) 03E35, 30L99 (Secondary) We show that the statement ``In every separable pseudometric space there is a maximal non-strictly δ-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and Górka in [M. Dybowski and P. Górka, The axiom of choice in metric measure spaces and maximal δ-separated sets, Archive for Mathematical Logic 62, 735-749, 2023.]. We also prove several related results. |
| title | Maximal δ-separated sets in separable metric spaces and weak forms of choice |
| topic | Logic 03E25 (Primary) 03E35, 30L99 (Secondary) |
| url | https://arxiv.org/abs/2405.10466 |